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Chapter 35: Q19P (page 1075)

Suppose that Young’s experiment is performed with blue-green light of wavelength 500 nm. The slits are 1.20 mm apart, and the viewing screen is 5.40 m from the slits. How far apart are the bright fringes near the center of the interference pattern?

Short Answer

Expert verified

The bright fringes near the center of the interference pattern are apart of 2.25 mm.

Step by step solution

01

Write the given data from the question

Blue-green light Wavelength, λ=500nm.

The slit separation, d=1.20mm.

The screen distance from the slit, D=5.4m.

02

Determine the formulas to calculate how far apart the bright fringes near the center of the interference pattern

The condition for the maxima in Young’s experiment is given as follows.

dsinθ=mλ …… (1)

Here, d is the distance between the slits, λis the wavelength, mis the order, andθis the angular separation.

03

Calculate how far apart the bright fringes near the center of the interference pattern

The maximum vertical distance from the center of the pattern is given by,

tanθ≈sinθ=ymD

Substitute ymDfor sinθinto equation (1).

dymD=mλym=mλDd

Substitute 1 for m, 54 m for D, 500 nm for λand 1.20mmfor d into above equation.

ym=1×500×10-9×5.41.2×10-3=27×10-71.2×10-3=22.5×10-4m=2.25mm.

Hence the bright fringes near the center of interference pattern are apart of 2.25 mm.

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Most popular questions from this chapter

We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thickness can the coating have to do this?

In Fig, monochromatic light of wavelength diffracts through narrow slit S in an otherwise opaque screen. On the other side, a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light travels from the slit directly to A interferes with light from the slit that reflects from the mirror to A. The reflection causes a half-wavelength phase shift. (a) Is the fringe that corresponds to a zero path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the minor as seen from a point on the viewing screen, and then consider Young’s two-slit interference.)

In Fig. 35-38, sourcesand emit long-range radio waves of wavelength400m , with the phase of the emission from ahead of that from source Bby 90° .The distance rA from Ato detector Dis greater than the corresponding distance localid="1663043743889" rBby 100m .What is the phase difference of the waves at D ?

In a double-slit experiment, the fourth-order maximum for a wavelength of 450 nm occurs at an angle of θ=90°. (a) What range of wavelengths in the visible range (400 nm to 700 nm) are not present in the third-order maxima? To eliminate all visible light in the fourth-order maximum, (b) should the slit separation be increased or decreased and (c) what least change is needed?

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